/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; & CC Bordeianu, Univ Bucharest, 2007
   Support by National Science Foundation
*/
//  diff.c:  Differentiation with forward, central and  extrapolated
//  comment: results saved as x y1 y2 y3  

#include <stdio.h>
#include <math.h>
#define h 1e-5                            // stepsize for all methods
#define xmax 7                               // range for calculation
#define xmin 0
#define xstep 0.01                                   // stepsize in x

main() { 
	
  double dc, result, x;
  double f(double);                      // function we differentiate
	
  FILE *output;                              // save data in diff.dat
  output = fopen("diff.dat","w");
  for (x = xmin; x<= xmax; x+= xstep)  {
    fprintf(output,"%f\t", x);
		                                            // forward difference
    result = (f(x+h)-f(x))/h;                    
    fprintf(output, "%.10f\t", result);
		                                            // central difference
    result = (f(x+h/2)-f(x-h/2))/h;                 
    fprintf(output, "%.10f\t", result);
    result = (8*(f(x+h/4.)-f(x-h/4.))-(f(x+h/2)-f(x-h/2.)))/(3.*h);
		                                            // extrapolated diff
    fprintf(output, "%.10f\n", result);               
  }
  printf("data stored in diff.dat\n");
  fclose(output);
}                                                      // end of main

double f(double x)                       // function to differentiate
{ return(cos(x)); }